1month Practical Course

1
1-month Practical Course Genome
AnalysisEvolution and Phylogeny methods Centre
for Integrative Bioinformatics VU (IBIVU) Vrije
Universiteit Amsterdam The Netherlands www.ibivu.
cs.vu.nl heringa_at_cs.vu.nl
2
Bioinformatics

• Nothing in Biology makes sense except in the
  light of evolution (Theodosius Dobzhansky
  (1900-1975))
• Nothing in bioinformatics makes sense except in
  the light of Biology

3
Evolution

• Most of bioinformatics is comparative biology
• Comparative biology is based upon evolutionary
  relationships between compared entities
• Evolutionary relationships are normally depicted
  in a phylogenetic tree

4
Where can phylogeny be used

• For example, finding out about orthology versus
  paralogy
• Predicting secondary structure of RNA
• Studying host-parasite relationships
• Mapping cell-bound receptors onto their binding
  ligands
• Multiple sequence alignment (e.g. Clustal)

5
Gene conversion

• The transfer of DNA sequences between two
  homologous genes, most often by unequal crossing
  over during meiosis
• Can be a mechanism for mutation if the transfer
  of material disrupts the coding sequence of the
  gene or if the transferred material itself
  contains one or more mutations

6
Gene conversion

• Gene conversion can influence the evolution of
  gene families, having the capacity to generate
  both diversity and homogeneity.
• Example of a intrachromosomal gene conversion
  event
• The potential evolutionary significance of gene
  conversion is directly related to its frequency
  in the germ line. While meiotic inter- and
  intrachromosomal gene conversion is frequent in
  fungal systems, it has hitherto been considered
  impractical in mammals. However, meiotic gene
  conversion has recently been measured as a
  significant recombination process, for example in
  mice.

7
DNA evolution

• Gene nucleotide substitutions can be synonymous
  (i.e. not changing the encoded amino acid) or
  nonsynonymous (i.e. changing the a.a.).
• Rates of evolution vary tremendously among
  protein-coding genes. Molecular evolutionary
  studies have revealed an 1000-fold range of
  nonsynonymous substitution rates (Li and Graur
  1991).
• The strength of negative (purifying) selection is
  thought to be the most important factor in
  determining the rate of evolution for the
  protein-coding regions of a gene (Kimura 1983
  Ohta 1992 Li 1997).

8
DNA evolution

• Essential and nonessential are classic
  molecular genetic designations relating to
  organismal fitness.
• A gene is considered to be essential if a
  knock-out results in (conditional) lethality or
  infertility.
• Nonessential genes are those for which knock-outs
  yield viable and fertile individuals.
• Given the role of purifying selection in
  determining evolutionary rates, the greater
  levels of purifying selection on essential genes
  leads to a lower rate of evolution relative to
  that of nonessential genes.

9
Reminder -- Orthology/paralogy
Orthologous genes are homologous (corresponding)
genes in different species Paralogous genes are
homologous genes within the same species (genome)
10
Orthology/paralogy

• Operational definition of orthology
• Bi-directional best hit
• Blast gene A in genome 1 against genome 2 gene B
  is best hit
• Blast gene B against genome 1 if gene A is best
  hit
• ? A and B are orthologous

11
Old Dogma Recapitulation Theory (1866)

• Ernst Haeckel
• Ontogeny recapitulates phylogeny
• Ontogeny is the development of the embryo of a
  given species
• phylogeny is the evolutionary history of a
  species
• http//en.wikipedia.org/wiki/Recapitulation_theory

Haeckels drawing in support of his theory For
example, the human embryo with gill slits in the
neck was believed by Haeckel to not only signify
a fishlike ancestor, but it represented a total
fishlike stage in development. Gill slits are not
the same as gills and are not functional.
12
Phylogenetic tree (unrooted)
human
Drosophila
internal node
mouse
fugu
leaf OTU Observed taxonomic unit
edge
13
Phylogenetic tree (unrooted)
root
human
Drosophila
internal node
mouse
fugu
leaf OTU Observed taxonomic unit
edge
14
Phylogenetic tree (rooted)
root
time
edge
internal node (ancestor)
leaf OTU Observed taxonomic unit
human
Drosophila
fugu
mouse
15
How to root a tree
m
f

• Outgroup place root between distant sequence
  and rest group
• Midpoint place root at midpoint of longest path
  (sum of branches between any two OTUs)
• Gene duplication place root between paralogous
  gene copies

h
D
f
m
h
D
1
m
f
3
1
2
4
2
3
1
1
1
h
5
D
f
m
h
D
f-?
f-?
h-?
f-?
h-?
f-?
h-?
h-?
16
Combinatoric explosion
Number of unrooted trees
Number of rooted trees
17
Combinatoric explosion

• sequences unrooted rooted
• trees trees
• 2 1 1
• 3 1 3
• 4 3 15
• 5 15 105
• 6 105 945
• 7 945 10,395
• 8 10,395 135,135
• 9 135,135 2,027,025
• 10 2,027,025 34,459,425

18
Tree distances
Evolutionary (sequence distance) sequence
dissimilarity
5
human x mouse 6 x fugu 7 3
x Drosophila 14 10 9 x
human
1
mouse
2
1
1
fugu
6
Drosophila
human
mouse
fugu
Drosophila
Note that with evolutionary methods for
generating trees you get distances between
objects by walking from one to the other.
19
Phylogeny methods

• Distance based pairwise distances (input is
  distance matrix)
• Parsimony fewest number of evolutionary events
  (mutations) relatively often fails to
  reconstruct correct phylogeny, but methods have
  improved recently
• Maximum likelihood L PrDataTree most
  flexible class of methods - user-specified
  evolutionary methods can be used

20
Distance based --UPGMA
Let Ci and Cj be two disjoint clusters
1 di,j ?p?q dp,q, where p ? Ci and q ?
Cj Ci Cj
Ci
Cj
In words calculate the average over all pairwise
inter-cluster distances
21
Clustering algorithm UPGMA

• Initialisation
• Fill distance matrix with pairwise distances
• Start with N clusters of 1 element each
• Iteration
• Merge cluster Ci and Cj for which dij is minimal
• Place internal node connecting Ci and Cj at
  height dij/2
• Delete Ci and Cj (keep internal node)
• Termination
• When two clusters i, j remain, place root of tree
  at height dij/2

d
22

• Ultrametric Distances
• A tree T in a metric space (M,d) where d is
  ultrametric has the following property there is
  a way to place a root on T so that for all nodes
  in M, their distance to the root is the same.
  Such T is referred to as a uniform molecular
  clock tree.
• (M,d) is ultrametric if for every set of three
  elements i,j,k?M, two of the distances coincide
  and are greater than or equal to the third one
  (see next slide).
• UPGMA is guaranteed to build correct tree if
  distances are ultrametric. But it fails if not!

23
Evolutionary clock speeds
Uniform clock Ultrametric distances lead to
identical distances from root to leafs
Non-uniform evolutionary clock leaves have
different distances to the root -- an important
property is that of additive trees. These are
trees where the distance between any pair of
leaves is the sum of the lengths of edges
connecting them. Such trees obey the so-called
4-point condition (next slide).
24
Additive trees
In additive trees, the distance between any pair
of leaves is the sum of lengths of edges
connecting them Given a set of additive
distances a unique tree T can be constructed
For all trees if d is ultrametric gt d is
additive
25
Distance based --Neighbour-Joining (Saitou and
Nei, 1987)

• Guaranteed to produce correct tree if distances
  are additive
• May even produce good tree if distances are not
  additive
• Global measure keeps total branch length
  minimal
• At each step, join two nodes such that distances
  are minimal (criterion of minimal evolution)
• Agglomerative algorithm
• Leads to unrooted tree

26
Neighbour joining
y
x
x
x
y
(c)
(a)
(b)
x
x
x
y
y
(f)
(d)
(e)
At each step all possible neighbour joinings
are checked and the one corresponding to the
minimal total tree length (calculated by adding
all branch lengths) is taken.
27
Algorithm Neighbour joining

• NJ algorithm in words
• Make star tree with fake distances (we need
  these to be able to calculate total branch
  length)
• Check all n(n-1)/2 possible pairs and join the
  pair that leads to smallest total branch length.
  You do this for each pair by calculating the
  real branch lengths from the pair to the common
  ancestor node (which is created here y in the
  preceding slide) and from the latter node to the
  tree
• Select the pair that leads to the smallest total
  branch length (by adding up real and fake
  distances). Record and then delete the pair and
  their two branches to the ancestral node, but
  keep the new ancestral node. The tree is now 1
  one node smaller than before.
• Go to 2, unless you are done and have a complete
  tree with all real branch lengths (recorded in
  preceding step)

28
Parsimony Distance
parsimony
Sequences 1 2 3 4 5 6
7 Drosophila t t a t t a a fugu a
a t t t a a mouse a a a a a t a
human a a a a a a t
Drosophila
mouse
1
6
4
5
2
3
7
human
fugu
distance
human x mouse 2 x fugu 4 4
x Drosophila 5 5 3 x
Drosophila
mouse
2
1
2
1
1
human
fugu
human
mouse
fugu
Drosophila
29
Maximum likelihood

• If dataalignment, hypothesis tree, and under a
  given evolutionary model,
• maximum likelihood selects the hypothesis (
  tree) that maximises the observed data (
  alignment). So, you keep alignment constant and
  vary the trees.
• Extremely time consuming method
• We also can also test the relative fit to the
  tree of different models (Huelsenbeck Rannala,
  1997). Now you vary the trees and the models (and
  keep the alignment constant)

30
Distance methods fastest

• Clustering criterion using a distance matrix
• Distance matrix filled with alignment scores
  (sequence identity, alignment scores, E-values,
  etc.)
• Cluster criterion

31
Phylogenetic tree by Distance methods (Clustering)
1 2 3 4 5
Multiple alignment
Similarity criterion
Similarity matrix
Scores
55
Phylogenetic tree
32
Lactate dehydrogenase multiple alignment
Distance
Matrix 1 2 3 4
5 6 7 8 9 10 11 12
13 1 Human 0.000 0.112 0.128 0.202
0.378 0.346 0.530 0.551 0.512 0.524 0.528 0.635
0.637 2 Chicken 0.112 0.000 0.155 0.214
0.382 0.348 0.538 0.569 0.516 0.524 0.524 0.631
0.651 3 Dogfish 0.128 0.155 0.000 0.196
0.389 0.337 0.522 0.567 0.516 0.512 0.524 0.600
0.655 4 Lamprey 0.202 0.214 0.196 0.000
0.426 0.356 0.553 0.589 0.544 0.503 0.544 0.616
0.669 5 Barley 0.378 0.382 0.389 0.426
0.000 0.171 0.536 0.565 0.526 0.547 0.516 0.629
0.575 6 Maizey 0.346 0.348 0.337 0.356
0.171 0.000 0.557 0.563 0.538 0.555 0.518 0.643
0.587 7 Lacto_casei 0.530 0.538 0.522 0.553
0.536 0.557 0.000 0.518 0.208 0.445 0.561 0.526
0.501 8 Bacillus_stea 0.551 0.569 0.567 0.589
0.565 0.563 0.518 0.000 0.477 0.536 0.536 0.598
0.495 9 Lacto_plant 0.512 0.516 0.516 0.544
0.526 0.538 0.208 0.477 0.000 0.433 0.489 0.563
0.485 10 Therma_mari 0.524 0.524 0.512 0.503
0.547 0.555 0.445 0.536 0.433 0.000 0.532 0.405
0.598 11 Bifido 0.528 0.524 0.524 0.544
0.516 0.518 0.561 0.536 0.489 0.532 0.000 0.604
0.614 12 Thermus_aqua 0.635 0.631 0.600 0.616
0.629 0.643 0.526 0.598 0.563 0.405 0.604 0.000
0.641 13 Mycoplasma 0.637 0.651 0.655 0.669
0.575 0.587 0.501 0.495 0.485 0.598 0.614 0.641
0.000
33
How to assess confidence in tree
How sure are we about these splits?
34
How to assess confidence in tree

• Bayesian method time consuming
• The Bayesian posterior probabilities (BPP) are
  assigned to internal branches in consensus tree
• Bayesian Markov chain Monte Carlo (MCMC)
  analytical software such as MrBayes (Huelsenbeck
  and Ronquist, 2001) and BAMBE (Simon and
  Larget,1998) is now commonly used
• Uses all the data
• Distance method bootstrap
• Select multiple alignment columns with
  replacement
• Recalculate tree
• Compare branches with original (target) tree
• Repeat 100-1000 times, so calculate 100-1000
  different trees
• How often is branching (point between 3 nodes)
  preserved for each internal node?
• Uses samples of the data

35
The Bootstrap

• 1 2 3 4 5 6 7 8
• C C V K V I Y S
• M A V R L I F S
• M C L R L L F T
• 3 4 3 8 6 6 8 6
• V K V S I I S I
• V R V S I I S I
• L R L T L L T L

5
1 2 3
Original
4
2x
3x
1
1 2 3
Non-supportive
Scrambled
5
36
Phylogeny disclaimer

• With all of the phylogenetic methods, you
  calculate one tree out of very many alternatives.
  
• Only one tree can be correct and depict evolution
  accurately.
• Incorrect trees will often lead to more
  interesting phylogenies, e.g. the whale
  originated from the fruit fly etc.

37
Take home messages

• Orthology/paralogy
• Rooted/unrooted trees
• Make sure you know the issues around the UPGMA
  algorithm and the NJ algorithm
• Understand the three basic classes of
  phylogenetic methods distance, parsimony and
  maximum likelihood
• Make sure you understand bootstrapping (to asses
  confidence in tree splits)